Arithmetic Progressions on Edwards Curves

We look at arithmetic progressions on elliptic curves known as Edwards
curves. By an arithmetic progression on an elliptic curve, we mean
that the x-coordinates of a sequence of rational points on the curve
form an arithmetic progression. Previous work has found arithmetic
progressions on Weierstrass curves, quartic curves, and genus 2
curves. We find an infinite number of Edwards curves with an
arithmetic progression of length 9.